Druid is a three-dimensional
block building connection game played on the square grid. Deadlocks are resolved
by letting players build blocks over enemy pieces.

Rules

Druid is played on a 10x10 grid of squares. Two players, Black and White, own alternating sides of the board which bear their color. The board is initially empty.

Each player owns a number of the following types of stones of their color:

Sarsens (single unit cubes).

Lintels (three unit cubes long).

Players take turns placing one of their stones on the board. Stones must always be aligned with the board squares.

Sarsens can be placed directly on the board surface, or on top of any same-colored stone.

Lintels cannot be placed on the board surface, but must be elevated by stones at both ends so that they lie flat and sit directly upon exactly two units of same-colored stone. Figure A shows some legal lintel placements by way of example.

Figure A. Legal lintel placements.

The game is won by the player who completes a connected set of their stones between their sides of the board (see Figure B).

Figure B. A game won by Black.

Two stones are connected if they are the same color and occupy orthogonally adjacent board squares, irrespective of their relative heights. Only the topmost stone at each board square counts in any connection; upper connections cut lower connections (over/under rule).

A single move swap option is recommended.

Notes

The rules of lintel placement imply that if a lintel does not bridge a gap with its central unit, then it must sit on exactly one unit of enemy stone. This rule not only stops players from stacking lintels (an overly strong play) but means that players can build over enemy stones.

This is especially important on the square grid, which is susceptible to deadlock. The triple-unit lintels provide an escape route over enemy blocks just as stacked marbles do in Akron. It has not been proven that all local Druid deadlocks can eventually be defeated, but this appears to be the case so far.

Like Akron, the over/under rule lets us project the game to a two-dimensional game graph which greatly simplifies matters. However, the game graph must contain terminal pairs for both players simultaneously due to nature of the square grid and local deadlocks.

Figure C. A temporarily deadlocked 6x6 game and its game graph.

Figure C shows a temporarily deadlocked 6x6 game (left) and its game graph (right). If the White terminals were not present then this graph would appear to be cut and hence a win for White, however nothing is further from the truth; Black can force a win no matter who plays next.

Druid is not limited to the square grid, and can be played on any regular or semi-regular tiling using prismatic extrusions of the board tiles (irregular tilings make lintel design difficult). Lintels of different shapes and sizes can be used.

Figure D. Druid played on other tilings.

Figure D shows some possible sarsen and lintel arrangements on non-square tilings. The triangular grid (left) is an interesting case as end-support sarsens always touch along at least an edge, hence the three-unit lintel will never cut an enemy connection by straddling it from side to side on this grid.

Strategy and Tactics

Druid is a rich tactical game. The fact that lintels threaten to build over enemy stones means that forcing moves are common, and traps readily set for an unwary opponent.

It is usually good to begin the game by staking out a staggered path of well-spaced sarsens across the board, since sarsen placement is generally the only possible move in the early stages anyway.

Placing friendly sarsens separated by an empty space is a good compromise between threatening an immediate lintel placement and gaining territory. However, pieces separated one empty space from enemy stones may be vulnerable to forcing moves, as shown in Figure E.

Figure E. Forcing move a and fork b yield a connection.

Figure E (left) shows a typical sparse formation after the early stages of the game, with White to move. White move a forces Black to build their sarsen up a level or risk having a lintel build over it. White has gained a square of territory while Black has been forced to waste a move without gaining any territory. This is a common play.

White move b is a similar forcing move that gains territory, but it is also a fork that guarantees connection, and hence a very efficient play. If Black again decides to save their besieged sarsen by building upwards as shown, then White can place a lintel between a and b to connect their two groups (dotted line).

Note that Black could have performed a similar attack if it were their turn; as with most connection games, the momentum afforded by having the move in hand can be decisive.

Building upwards is an obvious way to block opponent’s lintel placements. However, lower-level blockers can be just as effective, unless they are forced to build up.

Figure F. Black blocks White to the left.

For example, Figure F (left) shows a situation in which White wishes to connect to the left side of the board, with Black to move. Black piece a blocks the higher-level White connection from the left. Black would like to build a lintel along the edge to remove the dangerous White sarsen, however doing so would raise the lower-level block a and give White an immediate lintel placement to connect.

Instead, move b (Figure F, right) is a much better play for Black. It forms a strong 2x2 group which threatens to clobber any enemy piece placed alongside it. If White’s connection stretches to the right side of the board they can play at c to win next turn, otherwise they must play elsewhere and Black can play at c to complete the block.

Figure G. Black forces a connection to the top.

Figure G (left) shows a common sequence of forcing moves that guarantee connection to an edge. Move a forces White to block upwards, move b forces an immediate block to the edge, and move c guarantees connection for Black. If White tries to block the immediate connection then Black can place a lintel to restore it. Move a was deceptively subtle; if White were not forced to first build upwards then piece c would be under threat of a White lintel.

Note that this example is similar in nature to Akron example F, but instead of using a forcing move to create a freedom, it is used in this case to both force upwards development and prepare a platform for future lintel placement. Akron and Druid share many similarities, both being three-dimensional connection games on the square grid with similar goals.

Figure H. White to play and win (left) with forcing move a (right).

Figure H (left) shows a mini puzzle with White to play and win. Even though Black appears to have the far stronger position, the turn in hand again proves decisive and Figure H (right) shows White’s killer move a that wins the game. Black is forced to build upwards, preventing any defense against White’s next lintel move (dotted).